Spatial organization in cyclic Lotka-Volterra systems

We study the evolution of a system of N interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing average size, [l(t)]similar to t(alpha) where alpha=3/4 (1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, [L(t)]similar to t(beta) with beta=1 and 2/3 for N=3 and 4, respectively. For N greater than or equal to 5, the system quickly reaches a frozen state with noninteracting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as win as an exact solution for N=3. Same relevant extensions are also analyzed.